Teaching Responsibilities 2019/20
Term 1: MA243 Geometry
Algebraic topology, in particular algebraic and Hermitian K-theory, topological Hochschild and cyclic homology, equivariant homotopy theory, calculus of functors.
- Witt vectors with coefficients and characteristic polynomials over non-commutative rings, with Achim Krause, Thomas Nikolaus and Irakli Patchkoria, preprint 2020
- Witt vectors, polynomial maps, and real topological Hochschild homology, with Kristian Moi and Irakli Patchkoria, preprint 2019.
- Hermitian K-theory of Mackey functors, real traces, and assembly, with Crichton Ogle, Annals of K-theory 4-2 (2019), 243--316. DOI 10.2140/akt.2019.4.243.
- Real topological Hochschild homology, with Kristian Moi and Irakli Patchkoria, preprint 2017.
- Comparing cyclotomic structures on different models for topological Hochschild homology, with Cary Malkiewich, Irakli Patchkoria, Steffen Sagave, Calvin Woo, Journal of Topology, 12 (2019), no. 4, 1146-1173.
- Higher equivariant excision, Advances in Mathematics, 309 (2017), 1-96.
- A Dundas-Goodwillie-McCarthy theorem for split square-zero extensions of exact categories, An alpine bouquet of algebraic topology, Contemp. Math. 708, Amer. Math. Soc., 2018.
- Parametrized higher category theory and higher algebra: Exposé I -- Elements of parametrized higher category theory, with Clark Barwick, Saul Glasman, Denis Nardin, Jay Shah, preprint 2016.
- Parametrized higher category theory and higher algebra: A general introduction, with Clark Barwick, Saul Glasman, Denis Nardin, Jay Shah, preprint 2016.
- Equivariant diagrams of spaces, Algebr. Geom. Topol. 16 (2016), no. 2, 1157-1202.
- Homotopy theory of G-diagrams and equivariant excision, with Kristian Moi, Algebr. Geom. Topol. 16 (2016), no. 1, 325-395.
- Equivariant calculus of functors and Z/2-analyticity of real K-theory, Journal of the Institute of Mathematics of Jussieu, Volume 15, Issue 4, October 2016, pp. 829-883.
- A relative h-principle via cobordism-like categories, An Alpine Expedition through Algebraic Topology , Contemp. Math. 617, Amer. Math. Soc., 2014.
- Stable real K-theory and real topological Hochschild homology, Phd thesis, 2012.
Recent research grants
Funding from German Research Foundation Schwerpunkt-programm 1786, 2018-2019.